I calibrated VG model and i found that the fit to market data is quite good...Anyway, when i transform price in implied volatility (with matlab blsimpv routine) i get that the fit isn't so good...The biggest problem is that for maturity =1 week the pattern of implied volatility isn't a smile but a sort of "reverse" smile and this seems very strange...Anyone has a suggestion for such situation?

That might be caused through numerical errors especially for very smalltimes like a week: the denominator in the BS terms is vol*sqrt(time),so you have 0.3*sqrt(7/365) ~ 0.04 for an ATM option with vol = 30%. So you try to calculate s th like cdfN(1/0.04) = cdfN(25) which can notbe done in a meaningful way to revert it, if it is naively implementedby the usual polynomial approximations only (which should not be thecase in Matlab: check what range is covered by the cdfN there). But you will need good exactness in your VG pricer to solve for the vol(especially it should not be oscillating). Be sure about that, espec forsmall times ...The easiest way is to ignore everything with expiry below 3 month (asthey have their own rights and even may not fit to VG).

Well, but i expected that a pure jump process like VG be useful in pricing option with very short maturity (like 1 week)...I'm wrong if i say that tipically jumps are added in order to consider extreme events in short time interval?

QuoteOriginally posted by: hoareWell, but i expected that a pure jump process like VG be useful in pricing option with very short maturity (like 1 week)...I'm wrong if i say that tipically jumps are added in order to consider extreme events in short time interval?No, you are not wrong. Consider splitting smile parameters (whatever model) into continuous + jump. During lifetime of derivative the contribution of jump << continuous; however, closer to maturity, the contribution of jumps increases (exponentially?) and finally you get jump ~ continuous, especially at times < 1 week. Since most models do not include jumps, the jumps show up in bad fit. If I would you, I would include jumps and introduce jump-mix parameter, which you fit as well.... First, you can get idea about term structure of this parameter and, second, think why it is so.